Yes , the actual problem is a " hum " sound.
Since the cable signal is digital, any 60Hz induced from the electrical wiring would not be heard as a hum since the interference is analog.
I once had a situation in a condo development that had a feeder running through it with taps in pedestals periodically to serve the units. The pedestals were located out on the street with the POCO transformers. The complaint was 60Hz hum bars rolling through the picture on all channels. The problem turned out to be that the feeder running underground from tap to tap was only grounded in a few places which allowed a large neutral current to be carried by the cable sheath from one end of the development to the other. Grounding each tap to the utility transformer ground solved the problem. What happens in the analog world is that the cable carrying a current on the sheath actually made a pretty good modulator and modulated the analog TV carriers with the 60Hz. And no, it did not affect the audio which is FM.
But back to your case, I can't see how noise induced on your coax drops could cause a hum in the audio. I'm assuming here that what you are installing is just normal CATV, not something that is fed from CATV then converted from digital to legacy analog like they might do for a motel or nursing home with cheapo vintage TVs.
-Hal